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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations
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by John R. Graef, Chuanxi Qian and Bo Yang PDF
Proc. Amer. Math. Soc. 131 (2003), 577-585 Request permission

Abstract:

In this paper, the authors consider the boundary value problem \begin{gather} \tag {E} x^{(2m)}(t)+(-1)^{m+1} f(x(t))=0, \quad 0<t<1, \\ \tag {B} x^{(2i)}(0)=x^{(2i)}(1)=0, \quad i=0,1,2,\cdots ,m-1, \end{gather} and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)–(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373–2379) are discussed.
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Additional Information
  • John R. Graef
  • Affiliation: Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403
  • Email: john-graef@utc.edu
  • Chuanxi Qian
  • Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
  • Email: qian@math.msstate.edu
  • Bo Yang
  • Affiliation: Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
  • Email: by2@ra.msstate.edu
  • Received by editor(s): April 16, 2001
  • Received by editor(s) in revised form: October 2, 2001
  • Published electronically: June 18, 2002
  • Communicated by: Carmen C. Chicone
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 577-585
  • MSC (2000): Primary 34B15
  • DOI: https://doi.org/10.1090/S0002-9939-02-06579-6
  • MathSciNet review: 1933349